Virtual flowmeter for a well

ABSTRACT

A technique includes inducing a distributed temperature change along a portion of a wellbore and measuring a time varying temperature along the portion of the wellbore due to the induced change. The technique includes determining a distributed flow rate in the portion based at least in part on the measured time varying temperature before the temperature reaches equilibrium.

This application claims the benefit under 35 U.S.C. §119(e) to U.S.Provisional Patent Application Ser. No. 61/306,671 entitled, “VIRTUALFLOWMETER USING DISTRIBUTED TRANSIENT TEMPERATURE MEASUREMENTS,” whichwas filed on Feb. 22, 2010, and is hereby incorporated by reference inits entirety.

BACKGROUND

The invention generally relates to a virtual flowmeter for a well.

A typical completed well includes a variety of downhole sensors thatacquire data indicative of reservoir properties, flow configurations,geomechanical properties, etc. A distributed temperature sensor is onesuch sensor. The distributed temperature sensor, which may involveelectrical and/or optical technologies acquires a spatially distributedtemperature profile over a particular region of interest of the well. Ascompared to individual or discrete sensors, a distributed temperaturesensor-based system has traditionally provided the ability to perform arelatively wider and more comprehensive analysis of conditions downhole.

SUMMARY

In an embodiment of the invention, a technique includes inducing adistributed temperature change along a portion of a wellbore andmeasuring a time varying temperature along the portion of the wellboredue to the inducing. The technique includes determining a distributedflow rate in the portion based at least in part on the measured timevarying temperature before the temperature reaches equilibrium.

In another embodiment of the invention, a system includes a distributedtemperature sensing system and a processing system. The processingsystem receives data from the distributed temperature sensor indicativeof a time varying temperature along the portion of the wellbore due toan induced distributed temperature change. The processing systemdetermines a distributed flow rate in the portion based at least in parton the time varying temperature before the temperature reachesequilibrium.

Advantages and other features of the invention will become apparent fromthe following drawing, description and claims.

BRIEF DESCRIPTION OF THE DRAWING

FIGS. 1 and 3 are flow diagrams depicting techniques to determine adistributed flow rate in a well according to embodiments of theinvention.

FIGS. 2 and 5 are schematic diagrams of wells according to embodimentsof the invention.

FIG. 4 depicts measured and modeled time constants versus flow rateaccording to embodiments of the invention.

DETAILED DESCRIPTION

In the following description, numerous details are set forth to providean understanding of some illustrative embodiments of the presentinvention. However, it will be understood by those skilled in the artthat various embodiments of the present invention may be practicedwithout these details and that numerous variations or modifications fromthe described embodiments may be possible.

In the specification and appended claims: the terms “connect”,“connection”, “connected”, “in connection with”, and “connecting” areused to mean “in direct connection with” or “in connection with via oneor more elements”; and the term “set” is used to mean “one element” or“more than one element”. Further, the terms “couple”, “coupling”,“coupled”, “coupled together”, and “coupled with” are used to mean“directly coupled together” or “coupled together via one or moreelements”. As used herein, the terms “up” and “down”, “upper” and“lower”, “upwardly” and downwardly”, “upstream” and “downstream”;“above” and “below”; and other like terms indicating relative positionsabove or below a given point or element are used in this description tomore clearly describe some embodiments of the invention.

Systems and techniques are disclosed herein for purposes of constructinga virtual flowmeter for a well based on distributed transienttemperature measurements. More specifically, in accordance withembodiments of the invention described herein, a distributed temperaturesensing (DTS) sensor, which includes at least one optical fiber, isdeployed downhole to traverse a particular region of interest forpurposes of acquiring spatially distributed temperature measurements inthe region of interest. A pressure perturbation is introduced into thewell, which induces a temperature change in the region of interest; andas described below, data provided by the DTS sensor indicative of theresulting time varying temperature measurements are processed forpurposes of determining a distributed flow rate in the region ofinterest.

Referring to FIG. 1, thus, in accordance with embodiments of theinvention described herein, a technique 10 includes deploying (block 14)a distributed temperature sensor in a well and inducing (block 18) apressure change in the well. The distributed temperature sensor is usedto observe a variation in time of temperature due to the pressure changebefore the temperature reaches equilibrium, pursuant to block 22. Basedon the observed variation in time of the temperature before equilibrium,a distributed flow rate in the well is determined, pursuant to block 26.

As a more specific example, FIG. 2 depicts an exemplary well 100, whichincludes a DTS-based system for purposes of measuring a spatiallydistributed temperature profile along a region of interest of the well100. In this regard, in accordance with some embodiments of theinvention, the well 100 includes a wellbore 108, which may include acased portion 104 a (lined and supported by a casing 108) and an uncasedportion 104 b that extends downhole from the cased portion 104 a. Theabove-mentioned DTS-based measurement system includes a surface-disposedlaser interrogation and processing workstation 150 (herein called the“workstation 150”) and an optical fiber 158 that is optically coupled tothe workstation 150. The optical fiber 158 extends down into the well100 and extends through one or more regions of interest, as furtherdescribed below. It is noted that the optical fiber 158 may be disposedinside a relatively small diameter conduit, which may be filled with aninert gas, for example.

The DTS system may use another type of distributed temperature sensor inother embodiments of the invention; or alternatively, in accordance withother implementations, spatially distributed downhole temperaturemeasurements may be acquired using another type of sensor system, suchas an array of discrete pressure sensors, for example.

In this regard, a series of high-resolution temperature sensors may bedeployed along the sandface of an openhole completion to form adistributed temperature array. These sensors may have an associatedaccuracy and resolution that equals or exceeds the accuracies of fiberoptic distributed temperature measurements. Stable, high-resolutiondigital measurements may be made using such sensors in combination witha ratiometric circuit. The resulting apparatus, for example, may have aresolution of about 1 mdegC when sampled every minute. Sampling over alonger interval may result in a still higher resolution.

The temperature sensor system may also be deployed into other completionconfigurations whether or not the sandface is cased. For applicationswhere the wellbore is to be perforated, the sensor system may beoriented with respect to some internal key that is subsequently used toorient the perforating guns away from the area containing the sensors.For deployment into an open hole wellbore, the sensor system may beclamped and protected while running in, as well as being well thermallygrounded to the completion through the use of gold-coated sleeves, forexample. The sensor system may be placed in the vicinity ofinflow-control devices where the sensor system may measure thetemperature of the completion downstream of the incoming fluid. Thesensor system may also be deployed in the vicinity of active flowcontrol valves. In some embodiments, the sensors may be deployedexterior to the completion, or deployed into the interior of thecompletion. In the later case the sensors may be permanently installed(such as located along a stinger or dip-tube placed into the wellbore)or temporarily installed (for example deployed as part of a slickline orcoiled tubing intervention.

For rapid deployment in rigs with a high data rate, the sensor systemmay include temperature sensors that are assembled into a spoolablearray with the spacing largely determined before the spool istransmitted to the rig. Assembly and use of such arrays has beendisclosed, for example, in U.S. patent application Ser. No. 11/767,908,entitled, “PROVIDING A SENSOR ARRAY,” which was filed on Jun. 25, 2007,and is incorporated herein by reference. The spoolable array might befurther adjustable on the rig through the use of rig splicing andwelding apparatus, for example, such as through the use of knowntechnologies such as the Intellite family of connectors provided bySchlumberger. The spoolable array may also be deployed in combinationwith swellable packers.

The sensor array data may be passed along a multi-staged completionthrough the use of one or more inductive couplers, for example. However,inductive coupling may not be used, in accordance with other embodimentsof the invention.

Regardless of the form of the temperature sensor system, the sensorsystem is activated after completion of the wellbore.

For the exemplary well 100 of FIG. 2, the DTS-based system includes theoptical fiber 158 that extends downhole along a production tubingstring, herein called the “production tubing 112.” As a non-limitingexample, the optical fiber 158 may be attached to the outer surface ofthe production tubing 112 for purposes of obtaining various distributedtemperature measurements along the length of the production tubing 112.More specifically, in accordance with some embodiments of the invention,the production tubing 112 and optical fiber 158 extend through variousproduction zones 118 (zones 118 a and 118 b, being depicted asnon-limiting examples), which extend through corresponding formations.As an example, each of the production zones 118 form a correspondingregion of interest for which a set of spatially distributed temperaturemeasurements is acquired and a corresponding spatially distributed flowrate is determined.

As an example, the upper production zone 118 a may be an isolated zonethat is formed between an upper packer 130 that forms an annular sealbetween the exterior surface of the production string 112 and theinterior surface of the casing 108, and a lower packer 134 that forms anannular seal between the exterior surface of the production string 112and the uncased wellbore wall. The production zone 118 b may be formed,for example, below the packer 134, and another packer (not shown in FIG.2) may be disposed on the lower end of the production zone 118 b.

In accordance with some embodiments of the invention, each productionzone 118 is associated with various production/completion equipment 122(equipment 122 a and 122 b, being depicted in FIG. 2 as examples) forpurposes of regulating the flow of well fluid into the centralpassageway of the production string 112. As examples, the equipment 122may include various valves (sliding sleeve valves, ball valves, etc.),chokes, screens, shrouds, etc., as can be appreciated by the skilledartisan. For the specific example depicted in FIG. 2, the equipment 122may be provided at a particular location as part of the productionstring 112. Although other arrangements are contemplated, such asembodiments in which the equipment 122 may be part of an outer string orcasing, depending on the particular implementation.

For purposes of constructing the virtual flowmeter, the well 100includes, in addition to the DTS system, a device to introducetemperature changes in the zones 118. One way to introduce thesetemperature changes is to introduce a pressure perturbation in the well100 via a pressure changing device, such as a flow control valve or asurface-disposed wellhead valve 102. In this manner, the wellhead valve102 may be controlled by the workstation 150 for purposes of inducing apressure change at the wellhead to, in turn, induce pressure changes inthe various regions of interest downhole in the well. For this purpose,the workstation 150 includes a controller 151 that, in general, controlsoperation of the valve 102 and, in general, may control the DTS systemand the processing of the data gathered from the DTS system for purposesof determining a distributed flow in the well. Although the controller151 (as part of the workstation 150) is depicted as being disposed atthe well site, it is noted that this is merely an exemplary embodiment,as the controller 151 may be remotely located with respect to the well100, may employ a distributed architecture in which remotely and/orlocally disposed units coordinate the processing of the distributed flowrate, etc. Thus, many variations are contemplated and are within thescope of the appended claims.

In general, the controller 151 includes a processor 152 (a computersystem, a microprocessor, a microcontroller, a central processing unit(CPU), one or more processing cores, etc.) which execute instructionsthat are stored in a memory 153 of the controller 151 for purposes ofperforming all or portions of the techniques that are disclosed herein,such as one or more parts of the technique 10, which is discussed above.As also shown in FIG. 2, in accordance with some implementations, thecontroller 151 interacts with a laser interrogator 154 for purposes ofinteracting with the optical fiber 158 to launch optical pulses andreceive corresponding distributed temperature measurement data, inaccordance with some embodiments of the invention.

In accordance with some embodiments of the invention, the controller 151controls the operation of the wellhead valve 102 such that after thewell is brought into production at a certain flow rate, the controller151 changes the pressure at the wellhead outlet so that there is adifferent drawdown across the sandface (i.e., the interface at thewellbore wall in each of the zones 118). Because of the Joule-Thomsoneffect on the well fluid, the induced pressure change corresponds to anew inflow temperature. The inflow temperature does not, however, changeinstantaneously, but rather, the temperature is subject to a transientchange until the temperature stabilizes at an equilibrium temperature.The temperature measurements are therefore subject to a transienttemperature, which may be approximated by an exponential curve.

The time constant of the exponential is indicative of the heat-transfercoefficient of the region of the completion near that temperaturemeasurement. The time constant may be derived, as described herein,without knowledge of the equilibrium temperature, thereby permittingrelatively fast derivation of the determined flow rate. In general, theheat-transfer coefficient is dominated by two components: a conductiveterm, which describes the heat flow into the near wellbore zone; and aconvective term, which is proportional to the mass flow rate. Thislatter convective term varies as the flow-rate varies, whereas theconductive term is relatively constant. Consequently, by measuring thetime constant for a series of induced pressure changes (such as wellheadpressure-induced changes), the distributed flow rate in the vicinity ofthe temperature sensor (i.e., the optical fiber 158 in the region ofinterest) may be determined.

In accordance with some embodiments of the invention, the controller 151may apply calibration coefficients to convert the determined timeconstant to a distributed flow rate (e.g., the variation of the heattransfer coefficient along the wellbore). These calibration constantsmay be determined by noting that the overall flow rate along thewellbore gives rise to the measured flow rate along the wellbore. Byperforming this operation on all of the temperature measurement points,the controller 151 may derive a distributed mass flow rate along aregion of interest. In accordance with some embodiments of theinvention, the controller 151 displays the determined distributed flowrate on a display (now shown) of the workstation 150.

When the well 100 is first brought online the acquired temperaturemeasurements may form a near linear curve representing the geothermalgradient of the reservoir. In other cases, the wellbore may demonstratethat a temperature equilibrium state might be reached in the presence ofcross-flowing zones. In gas wells that have selectively low verticalpermeability, the drilled well itself might be the cause of thecross-flow, as the upper zones will have colder denser gas that cantravel down the wellbore to displace warmer, lighter gas in the lowerzones. In other wells, it is possible that there are different reservoirlayers that have anomalous pressures, in which case again the drillingof the wellbore initiates a cross-flow.

Bringing the well 100 into production triggers a different movement offluids in the wellbore and a corresponding change in pressure drawdownfrom reservoir pressure into the wellbore. Additional pressure drop mayarise along the wellbore via friction drop, gravity and turbulence andkinetic energy consideration. Wellbore simulation programs to modelthese effects may be provided with varying layers of complexity fromfairly rapid “nodal analysis” programs to more sophisticated but slowercomputational fluid dynamics packages. The computation of drawdown inthe reservoir may be performed with different degrees of sophisticationin the simulator. The wellbore and reservoir simulators may be providedfor both transient and pseudo-steady state models. In many cases, thetrue equilibrium will not be reached but can be approximated by apseudo-steady state formulation.

The temperature change introduced in a given zone 118 due to thepressure perturbation that is introduced by operation of the valve 102is due to the fact that reservoir fluids change temperature as theyundergo an iso-enthalpic pressure change. This is not the case for anideal gas, but is true of real gases, as well as liquids such as waterand hydrocarbons. The ratio of temperature change to pressure changeunder iso-enthalpic circumstances is termed the “Joule-Thomsoncoefficient.” For a typical reservoir configuration, the Joule-Thomsoncoefficient of a gas is positive (i.e., a decrease in pressure leads toa decrease in temperature), whereas the Joule-Thomson coefficients ofwater and hydrocarbon are negative. Joule-Thomson coefficients typicallyvary with both temperature and pressure, and empirical relationships maybe determined. Formulations may also be determined for the Joule-Thomsoncoefficient of a mixture (i.e., the coefficient of the mixture need notbe simply the weighted average of the individual coefficients).

By measuring downhole Joule-Thomson coefficients, it is possible to makeinferences of the fluid properties (e.g. to distinguish between gas andwater, or between oil and water). In particular, changing the wellheadpressure changes the downhole pressure. The reservoir pressure changesrelatively slowly meaning that wellhead pressure changes inducecorresponding changes in the drawdown pressure and hence, changes theJoule-Thomson effect on temperature. Therefore, changing the wellheadpressure induces a temperature transient, and if the equilibriumtemperature is known, or computed, then it is possible to derive flowrate. Unfortunately, it may be difficult to determine the equilibriumtemperature, and it may take a relatively long time to reach thattemperature. Any change in fluid properties or wellhead pressure duringthe intervening time results in a new equilibrium temperature.Therefore, the techniques and systems that are described herein considerthe use of multiple measurements of pressure and temperature during thedecay process (i.e., before equilibrium is reached) and apply a modifiedProny or other similar algorithm.

Prony's Method is essentially a decomposition of a signal with M complexexponentials via the following process:Regularly sample {circumflex over (f)} so that the n^(th) of N samplesmay be written as follows:

$F_{n} = {{\hat{f}( {\Delta_{t}n} )} = {\sum\limits_{m = 1}^{M}{B_{m}^{\lambda_{m}t}}}}$

If {circumflex over (f)} (t)happens to consist of damped sinusoids thenthere will be pairs of complex exponentials such that

$B_{a} = {\frac{1}{2}A_{i}^{\varphi_{i}j}}$$B_{b} = {\frac{1}{2}A_{i}^{{- \varphi_{i}}j}}$λ_(a) = σ_(i) + jω_(i) λ_(b) = σ_(i) − jω_(i) where $\begin{matrix}{{{B_{a}^{\lambda_{a}t}} + {B_{b}^{\lambda_{b}t}}} = {{\frac{1}{2}A_{i}^{\varphi_{i}j}^{{({\sigma_{i} + {j\omega}_{i}})}t}} +}} \\{{\frac{1}{2}A_{i}^{{- \varphi_{i}}j}^{{({\sigma_{i} - {j\omega}_{i}})}t}}} \\{= {A_{i}^{\sigma_{i}t}{\cos ( {{\omega_{i}t} + \varphi_{i}} )}}}\end{matrix}$

Because the summation of complex exponentials is the homogeneoussolution to a linear difference equation the following differenceequation will exist:

${\hat{f}( {\Delta_{t}n} )} = {- {\sum\limits_{m = 1}^{M}{{\hat{f}( {\Delta_{t}( {n - m} )} )}P_{m}}}}$

The key to Prony's Method is that the coefficients in the differenceequation are related to the following polynomial

${\sum\limits_{m = 1}^{M + 1}{P_{m}x^{m - 1}}} = {\prod\limits_{m = 1}^{M}( {x - ^{\lambda_{m}}} )}$

These facts lead to the following three steps to Prony's Method

1) Construct and solve the matrix equation for the P_(m) values:

$\begin{bmatrix}F_{N} \\\vdots \\F_{{2N} - 1}\end{bmatrix} = {- {\begin{bmatrix}F_{N - 1} & \ldots & F_{0} \\\vdots & \cdot & \vdots \\F_{{2N} - 1} & \ldots & F_{N - 1}\end{bmatrix}\begin{bmatrix}P_{1} \\\vdots \\P_{M}\end{bmatrix}}}$

Note that if N≠M a generalized matrix inverse may be needed to find thevalues P_(m)2) After finding the P_(m) values find the roots (numerically ifnecessary) of the polynomial

$\sum\limits_{m = 1}^{M + 1}{P_{m}x^{m - 1}}$

The m^(th) root of this polynomial will be equal to e^(λm).3) With the e^(λm) values the F_(n) values are part of a system oflinear equations which may be used to solve for the B_(m) values:

$\begin{bmatrix}F_{k_{1}} \\\vdots \\F_{k_{M}}\end{bmatrix} = {\begin{bmatrix}( ^{\lambda_{1}} )^{k_{1}} & \ldots & ( ^{\lambda_{M}} )^{k_{1}} \\\vdots & \cdot & \vdots \\( ^{\lambda_{1}} )^{k_{M}} & \ldots & ( ^{\lambda_{M}} )^{k_{M}}\end{bmatrix}\begin{bmatrix}B_{1} \\\vdots \\B_{M}\end{bmatrix}}$

where M unique values k_(i) are used. It is possible to use ageneralized matrix inverse if more than M samples are used.In the case that the pressure at the wellhead is not piecewise constant,a convolution approach may be employed, where each small variation ofpressure results in an additional exponential change; and thecombination overall is that the temperature transient is a convolutionof the pressure against computable kernels. Modifications to the Pronymethod are well known in the industry, for example, the Prony techniquecan be stabilized through the use of Singular Value Decomposition asdescribed in “Application of the singular valve decomposition—Pronymethod for analyzing deep-level transient spectroscopy capacitancetransients”, in Review of Scientific Instrumentation, vol 69, Issue 6,pp. 2459 by M. S. Mazzolo et al, the contents of which are herebyincorporated by reference.

A key aspect of the inversions is that an effective time constant may bederived without requiring waiting for a steady-state equilibriumpressure to be obtained. The temperature change along the wellbore isdistributed in nature and is not caused by a local temperature sink. Theflow rate in the wellbore may thus, be determined by the controller 151by the controller 151 matching the measured temperature transientsagainst a combined model of the wellbore and near-wellbore. Exemplaryparameters that may be used in the model are as follows:

Air:k_(f)=24×10⁻³ Wm⁻¹K⁻¹; μ=18×10⁻⁶ Nsm⁻²; ρ=1.29 kgm⁻³; c=1000Jkg⁻¹K⁻¹

Water:k_(f)=0.61 Wm⁻¹K⁻¹; μ=1×10⁻³ Nsm⁻²; ρ=1000 kgm⁻³; c=4000 Jkg⁻¹K⁻¹

Oil:k_(f)=0.13 Wm⁻¹K⁻¹; μ=2.5×10⁻³ Nsm⁻² at T=25° C.; ρ=900 kgm⁻³;c=1700 Jkg⁻¹K⁻¹

In many cases, matching the observed temperature transient to adistributed flow rate relies on additional parameters of the wellbore.For example, referring generally to FIG. 4, which depicts monitored data250 and a linear approximation 254 to the data 250, there are twoparameters required for the fit of linear approximation 254 to the data250. In particular, the heat-transfer coefficient from the wellborefluid to the completion may be a dominant factor in that linearapproximation. This raises a complication which has not been previouslyknown.

It is reasonable, however, to assume these coefficients vary only slowlyalong the wellbore. For example, if neither tubing material, tubingdiameters nor the lithology exterior to the completion has significantlychanged, then the heat-transfer coefficient may be assumed to change byan insufficient degree. By having a multiplicity of temperature sensors,then there are more measurements than unknowns. This allows thecontroller 151 to simultaneously determine heat transfer coefficientsand flow rates from a multiplicity of transient measurements along thewellbore.

The pressure may be induced by mechanisms other than the wellhead valve102. For example, FIG. 5 depicts a well 300 in accordance with otherembodiments of the invention. The well 300 has a similar design to thewell 100, with similar reference numerals being used to denote similarcomponents. However, unlike the well 100, the well 300 includes variousflow control devices 304 which are distributed along a production string301 (replacing the production string 112) and are activated in a way bythe controller 151 for purposes of changing the flow rate along thewellbore. These changes provide a pressure change along the wellbore andtherefore, induce a distributed temperature transient along the entirewellbore. In other embodiments of the invention, temperature sensors maybe disposed along with passive inflow control devices so that a flowmeasurement may be made downstream of the fluid entry.

Although a distributed flow rate may be determined before thetemperature measurements have reached equilibrium, additionalinformation is available once the measurements have reached equilibrium.In this manner, the controller 151 may further apply DTS processingbased on measured equilibrium temperatures for purposes of iterating aforward modeling package to find an optimal set of reservoir properties,which match the synthetic data with the measured data.

The heat-transfer coefficient may be viewed as the parallel sum ofindividual heat-transfer components. For example, there may be fluidmovement interior and exterior to the tubing. Or, in some cases, theremay be a cement sheath or gravel exterior to the tubing. The heatcoefficients for such composites may be computed. For the purposes offlow computation, one of the more important relationships is when thereis turbulent flow inside the tubing. In this case the conversion fromheat-transfer to flow-rate is straightforward.

For example, the heat transfer coefficient may be described as follows:

h=k/D Nu,  Eq.1

where “k” represents the thermal conductivity; “D” represents thehydraulic diameter and “Nu” represents the Nusselt number. The hydraulicdiameter of a smooth cylinder is equal to its measured diameter. Formore complicated duct profiles the hydraulic diameter can be computed.

The Nu Nusselt number can be related to the Reynolds number (called“Re”) as follows:

Nu=0.023 Re^(0.8) Pr^(n),  Eq.2

where “n” represents a coefficient that is, for example, 0.4 when thewall is hotter than the wellbore and 0.3 when the wellbore is hotterthan the well; and “Pr” represents the Prandtl number. The Reynoldsnumber may be described as follows:

$\begin{matrix}{{{Re} = \frac{v\; D}{\mu \; A}},} & {{Eq}.\mspace{14mu} 3}\end{matrix}$

where “μ” represents the fluid viscosity, and “v” represents the massflow rate.

The Prandtl number may be described as follows:

$\begin{matrix}{{\Pr = {C_{p}\frac{\mu}{\kappa}}},} & {{Eq}.\mspace{14mu} 4}\end{matrix}$

where “C_(p)” represents the heat capacity at constant pressure.

Other relationships may be used as well. For example, Gnielinksi'scorrelation may be described as follows:

$\begin{matrix}{{{Nu}_{D} = \frac{( {f/8} )( {{Re}_{D} - 1000} )\Pr}{1 + {12.7( {f/8} )^{1/2}( {\Pr^{2/3} - 1} )}}},} & {{Eq}.\mspace{14mu} 5}\end{matrix}$

where “Nu_(D)” represents the Nusselt number for a tube of diameter D;“f” represents the friction factor along the tubing; “Pr” represents thePradntl number; and “Re_(D)” represents the Reynold's number for theflow in the tube. This correlation is valid for Pr>0.5 and Re>3000 andso has broad applicability to hydrocarbon modeling in reservoirs. Thefriction factor may be obtained from a Moody diagram. Note that thederivation of flow rate becomes a nonlinear process, because thefriction factor is also dependent on flow-rate. Solutions of thatnonlinear equation can be done by standard techniques such as Newton'smethod.

Thus, referring to FIG. 3, to summarize, the controller 151 may performa technique 200 that is set forth in FIG. 3 for purposes of determininga distributed flow rate, in accordance with some embodiments of theinvention. Pursuant to the technique 200, the controller 151 induces atemperature transient phenomenon on one or more sensors that aredeployed along the sandface, pursuant to block 204. For example, thecontroller 151 may actuate the wellhead valve 102 or one or moredownhole flow control valves. Next, based on the observed temperaturemeasurements, the controller 151 calculates the characteristic timeconstants of the temperature transient, pursuant to block 208. Thecontroller 151 next uses (block 212) the time constants to deriveassociated heat transfer coefficients and determines (block 216) theNusselt number, which relates convective to conductive heat losses basedon the heat transfer coefficients. The controller 151 further determines(block 220) the Reynold's number based on the determine Nusselt numberand then determines (block 224) the mass flow rate based on theReynold's number.

Other embodiments are contemplated and are within the scope of theappended claims. For example, a system to construct a virtual flowmeterin accordance with other embodiments of the invention includes acombination of distributed temperatures sensors, a surface modelingpackage and downhole flow control devices. In these embodiments of theinvention, flow control devices are activated in such a way as to changethe flow along the wellbore. The change in flow provides a pressurechange along the wellbore and so induces a distributed temperaturetransient along the entire wellbore. In other embodiments of theinvention, the system includes temperature sensors along with passiveinflow control devices so that a flow measurement can be made downstreamof the fluid entry.

Additional information is available after the sensors have reachedequilibrium, because then traditional DTS processing may be moreapplicable. This processing may be enhanced through the use of aninterpretation workstation. The workstation enables the iteration of aforward modeling package to find an optimal set of reservoir propertiesthereby matching synthetic (or modeled) data with measured (or actual)data. This data may be combined by stabilizing the inversion forflow-rate using standard depth-based approaches.

In some scenarios, there may be a flow that is exterior to the string,e.g., along the annulus between string 112 and reservoir. In thisscenario, there is heat transfer from inside and outside the string 112.This flow may be enhanced for purposes of reading the correspondingtemperature transients through the use of dedicated components along thecompletion with an increased surface area on the side desired formaximum sensitivity to flow.

In yet other embodiments of the invention, temperature measurements maybe made at discrete time-intervals during the production of thereservoir. In such a scenario, it may be appropriate to consider thatthe conductive components of heat-transfer have not changed, in whichcase the remaining parameters to be adjusted would be the fluidproperties (oil, water, etc) or the reservoir properties. Integrationwith a reservoir modeling code may be one of the more optimal waysforward in that scenario. In some scenarios, it may be important toconsider that heat-transfer coefficients are changing in a mannerunrelated to flow, for example, if there is paraffin deposition in thevicinity of the temperature sensing. In this case, taking a multiplicityof flow-rates can be used to resolve the uncertainty.

Pressure measurements may also be made at the toe and heel of the wellto further stabilize the inversion. It is anticipated that a pressureloss is roughly proportional to the square of the fluid velocity.Because the flow is iso-enthalpic, this means that there will becorresponding temperature changes due to the Joule-Thompson process. Therelationship between a change in pressure and a change in temperature isindicative of the fluid type (e.g. water cut). Knowledge of the watercut may be used to refine the coefficients used for the empiricalrelationships between heat-transfer, Nusselt number and Reynolds'snumber.

While the present invention has been described with respect to a limitednumber of embodiments, those skilled in the art, having the benefit ofthis disclosure, will appreciate numerous modifications and variationstherefrom. It is intended that the appended claims cover all suchmodifications and variations as fall within the true spirit and scope ofthis present invention.

1. A method comprising: inducing a distributed temperature change alonga portion of a wellbore; measuring a time varying temperature along theportion of the wellbore due to the inducing; and determining adistributed flow rate in the portion based at least in part on themeasured time varying temperature before the temperature reachesequilibrium.
 2. The method of claim 1, wherein the inducing compriseschanging a wellhead pressure.
 3. The method of claim 1, wherein theinducing comprises controlling flow devices in the well.
 4. The methodof claim 1, wherein the measuring comprises receiving data from an arrayof sensors provided along the portion of the wellbore.
 5. The method ofclaim 1, wherein the measuring comprises receiving data from adistributed temperature sensor disposed along the portion of thewellbore.
 6. The method of claim 1, wherein the determining comprisesmodeling the temperature as an exponential function characterized by atime constant, determining the time constant and determining the flowrate based at least in part on the time constant.
 7. The method of claim6, further comprising applying a linear approximation to determine arelationship between the time constant and the distributed flow rate. 8.The method of claim 1, wherein the act of determining the distributedflow rate comprises: determining time constants of the temperature; anddetermining heat transfer coefficients based at least in part on thedetermined time constants.
 9. The method of claim 8, wherein the act ofdetermining the distributed flow rate further comprises: determining aNusselt number for a ratio of convective to conductive heat loss basedat least in part on the determined heat transfer coefficients.
 10. Themethod of claim 9, further comprising: determining a Reynold's numberbased at least in part on the Nusselt number.
 11. The method of claim10, wherein the act of determining the distributed flow rate furthercomprises: determining a mass flow rate based at least in part on theReynold's number.
 12. The method of claim 1, wherein the act ofdetermining the distributed flow rate comprises: determining a Nusseltnumber for a ratio of convective to conductive heat loss.
 13. The methodof claim 1, wherein the act of determining the distributed flow ratecomprises determining a Reynold's number.
 14. The method of claim 1,wherein a flow associated with the distributed flow comprises aturbulent flow.
 15. The method of claim 1, wherein a flow associatedwith the distributed flow rate is present in a production tubing,another flow is present in an annulus exterior to the production tubing,and the act of determining the distributed flow rate is based at leastin part on the flow in the production tubing and the flow in theannulus.
 16. The method of claim 1, wherein a flow associated with thedistributed flow rate has a time varying pressure drop induced by a timevarying flow rate.
 17. The method of claim 16, wherein the pressure dropinduces a change in temperature in the well due to an iso-enthalpicprocess.
 18. The method of claim 1, wherein the act of determining thedistributed flow rate is performed at intervals of time of hydrocarbonproduction and the act of determining the distributed flow rate is basedat least in part on a reservoir model, the method further comprising:refining the reservoir model based at least in part on a determinationof the flow rate at the intervals.
 19. A system comprising: adistributed temperature sensing system to measure a distributedtemperature along at least a portion of a wellbore; and a processingsystem to: receive data from the distributed temperature sensorindicative of a time varying temperature along the portion of thewellbore due to an induced distributed temperature change; and determinea distributed flow rate in the portion based at least in part on thetime varying temperature before the time varying temperature has reachedequilibrium.
 20. The system of claim 19, further comprising: a pressurechanging device to induce the temperature change.
 21. The system ofclaim 20, wherein the pressure changing device comprises awellhead-disposed valve or at least one downhole flow device.
 22. Thesystem of claim 19, wherein the processing system is adapted to: modelthe temperature as an exponential function characterized by at least onetime constant; determine the time constant; and determine thedistributed flow rate based at least in part on the determined timeconstant.
 23. The system of claim 19, wherein the processing system isadapted to: determine time constants of the temperature; and determineheat transfer coefficients based at least in part on the determined timeconstants.
 24. The system of claim 23, wherein the processing system isadapted to: determine a Nusselt number for a ratio of convective toconductive heat loss based at least in part on the determined heattransfer coefficients.
 25. The system of claim 24, wherein theprocessing system is adapted to: determine a Reynold's number based atleast in part on the Nusselt number.
 26. The system of claim 25, whereinthe processing system is adapted to: determine a mass flow rate based atleast in part on the Reynold's number.
 27. The system of claim 19,wherein the processing system is adapted to: determine a Nusselt numberfor a ratio of convective to conductive heat loss.
 28. The system ofclaim 19, wherein the processing system is adapted to: determine a massflow rate based at least in part on the Reynold's number.